以熱阻網路模型預測工具機主軸的熱變形

Abstract

工具機主軸的熱變形是影響加工精度的重要因素之一。工具機主軸在高速加工時，因軸承摩擦導致溫升，而使得主軸產生熱變形，進而影響加工精度。為了提升加工精度，使用熱補償技術是一種有效修正主軸熱變形誤差的方法。本文先利用物理理論和文獻中的經驗公式來簡化工具機主軸的理論模型，續以灰箱系統識別的方法來建立運算量遠低於有限元素法之熱阻網路模型。該熱阻網路模型可利用主軸轉速來預測主軸內部特徵點之溫度。而後採用該熱阻網路模型所預測之溫度和黑箱系統識別方法來建立預測主軸軸向熱變位的模型；該主軸軸向熱變位的模型係以狀態空間的數學結構表示之。最後再採用統計學中的相關係數法來簡化該主軸軸向熱變位的模型，使得原先需要輸入7個特徵點溫度的主軸熱變位模型簡化為僅需輸入3個特徵點溫度，可大幅所短運算量和時間。結合前述預測主軸溫度的熱阻網路模型和預測主軸熱變位的模型，即可利用主軸轉速預測工具機主軸軸向的熱變位，而模型預測曲線與實驗量測數據相比，誤差小於2 μm。

The thermal deformation of spindle is one of the important factors that affect the machining accuracy of machine tools. The friction of the bearings of spindle during high-speed machining causes the temperature rising and thermal deformation of spindle and thereby affects the machining accuracy. To improve the machining accuracy, the thermal compensation technology is a useful method to correct the machining error induced by the thermal deformation of spindle. The author firstly establishes a simplified theoretical model of the spindle based on physical principles and the empirical formula proposed by literatures and then adopts the method of grey-box system identification to establish the thermal network model of the spindle. The thermal network model can estimate the temperatures of 7 feature points within the spindle and its amount and time of numerical calculation are much lower than the finite element method. After that, by means of the method of black-box system identification, the temperatures of the 7 feature points estimated by the aforesaid thermal network model are used as the input data to training the thermal deformation model of the spindle. The resulting thermal deformation model is expressed in terms of state space and can estimate the axial deformation of the spindle. Finally, the author further simplifies the thermal deformation model of the spindle by means of the correlation coefficient method in statistics. The simplified thermal deformation model requires only the input temperature data of 3 feature points within the spindle. The simplified thermal deformation model further reduces the amount and time of numerical calculation while remaining the accuracy. The integration of the aforesaid thermal network model and thermal deformation model, one can estimate the thermal deformation of the spindle from its rotational speed. Comparing with the experimental measurement, the error of the estimated thermal deformation is less 2 μm. The proposed method of thermal deformation estimation is applicable to the thermal compensation of machine tool.